G L Mittal and TARUN MITTAL Solutions for Chapter: Units : Fundamental and Derived Units, Exercise 2: NUMERICALS

The earth has a mass of $5.98\times {10}^{24}kg.$The average mass of the atom of the earth is $40 \mathrm{u}$. How many atoms are in the earth?

The density of water at $4° \mathrm{C}$ is $1.00 \mathrm{g}/{\mathrm{cm}}^3$. Find its value in SI units.

The acceleration of a body is $10 \mathrm{m}/{\mathrm{s}}^2$. Express it in $\mathrm{km}/{\mathrm{h}}^2.$

The value of the universal gravitational constant is $6.67\times {10}^{-11} \mathrm{N} {\mathrm{m}}^2 {\mathrm{kg}}^{-2}$.  Find its value in ${\mathrm{g}}^{-1} {\mathrm{cm}}^3 {\mathrm{s}}^{-2}$.

The value of Stefan's constant is $\sigma =5.67\times {10}^{-5}{\mathrm{ergs}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{K}}^{-4}$. Find its value in SI units.

Express speed of light $(3.0\times {10}^8\mathrm{m}/\mathrm{s})$   in terms of AU per min.

If the speed of light is new unit of speed  and year is the new unit of time. Then what is the new unit of length? What is its name? Given that $\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}$ and year=$3.154\times {10}^7\sec .$

For a new unit of length, the speed of radio wave is unity. Find the distance of an aircraft from a RADAR, if the radio signals return back after reflection of aircraft in $8.4 \mathrm{\mu s}$.